Lebesgue Integral Overview

In this video, I present an overview (without proofs) of the Lebesgue integral, which is a more general way of integrating a function. If you'd like to see proods of the statements, I recommend you look at fematika's channel, where he gives a more detailed look of the Lebesgue integral. In another video, I will give a specific example of a function for which I'll calculate the Lebesgue integral. Enjoy!

[Hepad_]

FINALLY SOMEONE WHO PRONOUNCES IT RIGHT
The French "es" before a consonant is an old version of "ê", like "crêpe" was "crespe"
Like for the English "hospital, hospitalization", we have "hôpital, hospitalisation" :)

So "Lebesgue" comes from "le besgue" (the old way of writing "the stutterer") which became "le bêgue" !

Bonne vidéo !

[HuntBobo]

The best explanation of Lebesgue integration and measure theory I’ve heard, better than a month of class.

[Princesse-Chaos]

paused on 2:21 and I must say: Dr Peyam, you give off so much positive energy that I'm instantly so encouraged to understand the topic well and I think that many lecturers should learn how to engage their students like you do.

[wtt]

What a great video in which Sir has given more than clear explanations . The best video on the subject I have ever watched !

[justwest]

Very nice, writing my calc 3 exam tomorrow about measure theory and lebesgue integration. If you go deeper, you'll discover very powerful theorems like Fubini's or Transformation. I really advice everybody to study that field, it's awesome!

[won-tiwi]

so nice, you just saved one student struggling with real analysis
thanks..

[pedrohenriquesilvadossanto]

Sou do Brasil, e encontrei os seus videos somente hoje. Embora tenho certa dificuldade em entender o idioma, gostei muito das suas aulas e da forma como explica. Parabéns Professor!!

[madhavpr]

Mind = blown !! I just finished solving a lot of problems in my introductory real analysis text. Can't wait to get into measure theory.

[davidwright]

Thanks once again, Dr Peyam! A couple of requests: Could you please list videos referred to (links would be nice!), and also give some indication of sequence / dependency of yr videos. I know this may change as you insert stuff between topics covered, but I'm sure yo cna come up with a system that will help us all! As usual, very clear. Sahzoom til we meet again!

[earthperson]

11-12-2020. This is masterful and excellent! Great work.

[elhoplita]

I have watched several of your videos, I think you come across incredibly well and clear!

[vector]

This comment is directed at ALL OTHER YOUTUBERS who have posted videos on measure theory and the Lesbesgue integral:

Dr. Peyam has just shown you above how to teach this concept. Every other youtube math teacher starts by rehashing how the Riemann integral works--usually showing off their prowess by integrating a complicated function--and then they go down a list, axiomatically, of Lesbesgue concepts, usually descending into the depths of PROVING THEM ONE BY ONE, thereby losing the attention of the viewer.

Then they close by verbally stating that the Lesbesgue integral simplifies and generalizes integration, but providing no graphic demonstration.

That's the abstract nonsense that normally passes for a pedagogical video on the Lesbesgue measure.

Thank you Dr. Peyam, for your pedagogy and your enthusiasm.

[yellowjackets]

This guy is helping me get through quarantine

[Lance.]

Fematika is how you spell the channel, it's a good one for very high level pure math concepts

[karstenmeinders]

Looking forward to seeing a function where the Lebesque integral is easier than the Riemann integral.BTW: the whiteboard is much easier readily (as many others have stated already)

[sarkersunzidmahmud]

the visualization of dominated convergence theorem was top knotch.

[aartichowbey]

Looking forward to see more and more videos of lebesgue measure.

[cycklist]

I'd love a video on measures of sets.

[digitig]

The first rule of non-measurable functions is you don't talk about non-measurable functions.

[chessislife]

Great explanation, love your passion for math!